The development of a sound theory that predicts and verifies existing evolutionary algorithms (EA) is one of the most important research issues in the field today. In mathematical proofs, the assumption of spherical symmetry is probably one of the most widely used simplifications. This paper discusses the extent to which spherical symmetry is appropriate for certain EAs. It turns out that spherical symmetry leads to simplifications in (self-adaptive) EAs but seems inappropriate for certain genetic algorithm variants, since small mutation rates bias a search algorithm toward the coordinate axes. This paper also argues that current test suites are weak in that they do not provide problems with significant epistasis that describes the interaction between different parameters. Consequently, when using an empirical test for pushing existing theory beyond its limits, benchmark functions should include more epistatic interaction or at least should use coordinate rotations.

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